Amusing Monday: Puzzling over water jars

A classical puzzle about water jars begins with an 8-gallon jar full of water and two empty jars. One of the empty jars can hold exactly 5 gallons of water; the other can hold exactly 3 gallons. The goal is to use the three containers to divide the water equally, leaving 4 gallons in two separate containers.


This has always been a good brain-teaser. The puzzle can be altered and made more or less difficult as you change the number and size of the jars and vary the number of gallons you’re trying to end up with.

I’ve always tried to complete these puzzles in my head, but I recently discovered some fun ways of tackling these challenges. A variation on the puzzle above is to eliminate the 8-gallon jar but include the ability to fill and dump out the remaining jars whenever you choose.

Check out the interactive “Decanting Puzzle” on the “Math is Fun” website. Each level offers a different puzzle.


The classical version of this puzzle is the very one posed as a suspenseful life-and-death challenge in the movie “Die Hard III.” Remember the scene by the fountain? Watch this video segment of the movie by clicking here on the Videolab website.

I’ve never taken a mathematical approach to these puzzles, but lots of smart people have developed alternate ways to solve the problems. Alexander Bogomolny, former associate professor of mathematics at the University of Iowa turned software developer, explores several options on his webpage “Interactive Mathematics Miscellany and Puzzles.” Check out his descriptions of the “Three Jugs Puzzle.” If you enjoy math or are challenged by its concepts, follow the various links at the bottom of each page. I actually found myself intrigued by the section on barycentric coordinates.

Similar puzzles can be found at

In his introduction to the three jugs problem, Bogomolny shares the story of Siméon Denis Poisson (1781-1840), who tried out various professions with “singular ineptitude” until someone challenged him with the classical puzzle. He solved it immediately and became enthralled with the mathematical construct, going on to become one of the greatest mathematicians of the nineteenth century, working on celestial mechanics, probability, calculus, electricity and magnetism.